​​I would argue for postwestern, as I am thinking you refer to that amorphous thing we are still figuring out--an ethos, a moment, a phenomenon, right?  A theoretical framework?  Do you think Susan Kollin made a case for using a single, unhyphenated word in Postwestern Cultures​?  If so, there is precedent for this neologism.  If not, then of course that is interesting, too. 

If you are referring more specifically to something following the Western as a genre, then i would agree with Drucilla. But I understood your query differently.

Best,

Jennifer